1. Viper Probe Droid: You may play this unit from your discard pile as if it was in your hand.

Does this mean you can only "play" this as a unit from the discard pile during the Deployment Phase or are you also able to "place" this unit into the edge stack from discard pile during an edge battle.

I am going with only being able to use its ability during Deployment Phase due to the "play" wording, but I am wondering if maybe it was meant to be useable from discard during edge battles as well?

2. Leia Organa: If this unit leaves play, it is captured by your opponent at any dark side objective of his choice.
Interrupt: When this unit leaves play, remove all focus tokens from all cards you control.

You're My Only Hope: Action: Sacrifice a unit to draw 2 cards. Then, your opponent chooses and discards 1 card from his hand, if able.

Does Leia's ability trigger when Sacrificing her via a card like "You're My Only Hope" (in the same objective set)? She is leaving play via Sacrifice, but does Sacrifice have anything special about it ala M:tG.

I am going with sacrfice will trigger her ability so she is literally unable to go to discard pile unless randomly discarded from hand or deck or capture stack (only three places card can be without being in play)

1) "As if it were in your hand" suggests that you can only play it in the Deployment Phase, like any other unit. All other units that can be played at a special time (Admiral Ackbar, Human Replica Droid) have text telling you when they can be played.

2) Yes, if Leia is sacrificed for the effect of You Are My Only Hope, her Interrupt effect triggers. Same thing if you sacrifice her for Covering Fire.

To follow up on #1, since I'm not sure that first response was what you were asking: the probe droid only allows you to play it from the discard pile, so that is all you can do. Placing cards in edge battles is not playing them, so you cannot use a discarded probe droid in that way.